A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?

How can a man go eight days without sleep?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?

Below toothpicks/matchsticks indicate the group of fishes moving from west to east direction. Can you make them move from east to west by just moving three toothpicks/matchsticks?

I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

Here is what you have to do. You have to throw a ball as hard as you can but it must return back to you even if it does not bounce at anything. Also, you have nothing attached to the ball. There is no one on the other end to catch that ball and throw it back at you.

How will you do it?

I am a type of food that is often found in the fridge and can be white in colour. What I am?
Hint 1: I am a dairy product.
Hint 2: You can spread me on the bread.

Irene killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

A wooden log balances equally on the scales when weighed with three-quarters of a pound and three-quarters of a wooden log.

Can you calculate the weight of the entire wooden log?

Can you identify the famous TV character from the rebus below?